Based on the above analysis and comparison of DAM
retrieval performance, a set of desirable performance characteristics
can be identified. Figures 7.3.1 (a) and (b) present a conceptual
diagram of the state space for high- and low-performance DAMs,
respectively (Hassoun, 1993).
Figure 7.3.1. A conceptual diagram comparing the
state space of (a) high-performance and (b) low-performance autoassociative
The high-performance DAM in Figure 7.3.1(a) has
large basins of attraction around all fundamental memories. It
has a relatively small number of spurious memories, and each spurious
memory has a very small basin of attraction. This DAM is stable
in the sense that it exhibits no oscillations. The shaded background
in this figure represents the region of state space for which
the DAM converges to a unique ground state (e.g., zero state).
This ground state acts as a default "no decision" attractor
state where unfamiliar or highly corrupted initial states converge
to this default state.
A low performance DAM has one or more of the characteristics
depicted conceptually in Figure 7.3.1 b. It is characterized
by its inability to store all desired memories as fixed points;
those memories which are stored successfully end up having small
basins of attraction. The number of spurious memories is very
high for such a DAM, and they have relatively large basins of
attraction. This low performance DAM may also exhibit oscillations.
Here, an initial state close to one of the stored memories has
a significant chance of converging to a spurious memory or to
a limit cycle.
To summarize, high-performance DAMs must have the
following characteristics (Hassoun and Youssef, 1989): (1) High
capacity. (2) Tolerance to noisy and partial inputs. This implies
that fundamental memories have large basins of attraction. (3)
The existence of only relatively few spurious memories and few
or no limit cycles with negligible size of basins of attraction.
(4) Provision for a "no decision" default memory/state;
inputs with very low "signal-to-noise" ratios are mapped
(with high probability) to this default memory. (5) Fast memory
retrievals. This list of high-performance DAM characteristics
can act as performance criteria for comparing various DAM architectures
and/or DAM recording recipes.
The capacity and performance of DAMs can be improved
by employing optimal recording recipes (such as the projection
recipe) and/or using proper state updating schemes (such as serial
updating) as was seen in Section 7.2. Yet, one may also improve
the capacity and performance of DAMs by modifying their basic
architecture or components. Such improved DAMs and other common
DAM models are presented in the next section.
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